Same animation to different objects
Once you have animated the first object, select the other objects, then the animated object so that it is the active object (highlighted a brighter orange). Then press &#9096; CtrlL and choose Animation Data, this will give each object the same action.

You could also select each object and set the action in the action editor.



In the NLA editor, click the double down arrows for each object to turn the action into an NLA strip for each object.



You can now select and move G each NLA strip so that each object is animated at a different time. You can also set the start and end frames in the properties region N.